Finite Group DatabasebetaFinite Group Databasebeta| order | 5504 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C43×#500 ⋊ C2 |
| Sylow | C43 ⋊ Q8×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D43 |
| commutator | C2×C4×C43 | C24 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#500 | C2 |
| socle | C22×C43 | C22×D4 |
| hypercenter | #500 | D43 |
| hypocenter | C43 | Q8×D8 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #500 | |
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,43|a^2=e,b^2=e,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=de,f^c=fg,h^c=h^42,h^d=h^42497 conjugacy classes — view the full character table.
| maximal subgroup of | #25010270, #25010274, #25010298, … |
| maximal normal subgroup of | #25010270, #25010274, #25010298, … |
| maximal quotient of | #25113183, #25114989, #25114990, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5504, 17362);